For reference, this recent NPR article contains all of the information that inspired this question.
The lawsuits referenced in the above article center on then-President Trump blocking individual users on Twitter from interacting with or seeing his tweets. Lower courts apparently ruled that Trump's twitter feed is essentially a public forum, and therefore, blocking users was unconstitutional because it amounted to viewpoint discrimination. There haven't been (as far as I know) any lawsuits against Twitter for their banning of Trump while he was President. Clearly, any such lawsuits would likely be ruled moot now, but it stands to reason that if Trump isn't allowed to prevent people from interacting with him on social media, then Twitter shouldn't be allowed to prevent people from interacting with him either.
One possible distinction here is that Twitter wasn't practicing viewpoint discrimination since they effectively blocked everyone from interacting with President Trump without regard to viewpoint. However, if the President's presence turns a social media account into a public forum, then preventing the president from having an account seems to be a form of viewpoint discrimination in itself. Really, the whole thing is very strange since it seems to suggest that Twitter (a private company) has control over whether or not certain public fora are allowed to exist. To me, that sounds like those fora were never really "public" at all (meaning Trump should be able to block people from his personal account), or if they were, then Trump's viewpoint was being discriminated against and Twitter has an obligation as the purveyor of this public forum to protect his rights.
Why are Trump blocking individuals on Twitter and Twitter effectively blocking everyone for Trump by banning him treated differently under the law?